The answer to that is a hair bigger that the question. Spot colors are premixed colors or formula colors outside of cmyk. Theyve been around longer than cmyk ever was. Spot colors today are colors you generally can get with the standard cmyk model. Often you see them used in packaging to get a particular shade of color or in art posters where they use 1,2, or 3 or more colors (Dave Matthews band has some of the nicest posters that use spot colors). Pantone is a great example of spot colors - these are heavily incorporated into photoshop by the way. I personally use them for 2 and 3 tone photos.
Do you have to use them? Of course not. Can you use cmyk instead of spot colors? Sure, BUT there are lots of colors you can't duplicate with cmyk or rgb or even the hexachrome process. For example - metallic inks must be treated as a spot color. Look at a Pantone book, use photoshop to dup the colors, print via cmyk. Notice the colors don't match? If you don't have a Pantone book, look at the color swatches for many types of paint. In order to keep their colors unique from other brands, paint makers will use colors that don't reproduce easily.
If you are a serious designer and you plan to do something like package design, posters, or any serious printing, pick up the Pantone's Guide to Communicating with color. Now if you strictly do web work or digital work with no print, you won't need them until Pantone makes a spot color monitor. ;)
Forgot - overlapping spot colors are when you have one color over another - you can see the shadow of one color over another. Generally not desirable, but you see it used artfully from time to time. You see this in tshirt printing or screen printing in general. Since this will rapidly progress into a much larger topic and a discussion of how to do your bleeds and other printing terms. Sounds like you may need to pick up a graphic design 200 level book or look into a printing book.
Well, I'm not sure what to tell you. There are literally hundreds (if not thousands) of books out there on the subject. I would start with searching for simple things like "lithography," "offset lithography," "spot colors" and "pantone" in Wikipedia and go through their bibliography (or references) at the end. Even a simple search online will yield practical results. Given that you are a photoshop user, look into "spot colors in photoshop" as well. Sorry to be kinda dodgy about it, but there are tons of references out there and you shouldn't need to buy a book.